Many members are naturally hostile to the Conservatives and lean towards Labour; others have much in common with the Tories and abhor Labour. Getting those groups to agree a deal over the government of Britain and its policies could be a Herculean task.

Mr Clegg is a member of the Orange Book faction, a group of Lib Dem MPs who have fought to push the party towards the right in many areas. Yet while the Orange Bookers have been successful in Parliament, grassroots members tend to be more left-leaning.

They could be a significant obstacle to any deal with the Conservatives, particularly as the Lib Dems remain defiantly “democratic”, reflecting the will of card-carrying members through a complex party rule book.

Any Lib Dem leader making a power-sharing deal in a hung parliament faces a “triple lock” that he must open to get his party’s approval.

The rule says that “any substantial proposal which could affect the party’s independence of political action” must first be approved by its MPs and the party’s governing Federal Executives. Then, in most circumstances, a special party conference is required to give approval. And unless that conference votes two-for-one in favour of the deal, it must be approved by the entire party membership in a postal vote.

Lib Dem insiders play down the significance of the rules, arguing they give Mr Clegg a degree of discretion about how they are applied.

But in proposing any deal, he must still tread cautiously, for Lib Dem members relish the opportunity to defeat and defy their leaders.